Q.Consider a current carrying wire (current $I$) in the shape of a circle. Note that as the current progresses along the wire, the direction of $\mathbf{j}$ (current density) changes in an exact manner, while the current $I$ remains unaffected. The agent that is essentially responsible for this is

The key idea is Drift Velocity: the net velocity of charge carriers under an applied electric field, which determines current density $\mathbf{j}$.

1. Current density is $\mathbf{j} = n e \mathbf{v}_d$, where $\mathbf{v}_d$ is the drift velocity. Its direction is set by the local electric field $\mathbf{E}$ inside the wire.
2. In a circular wire, the wire's geometry forces $\mathbf{E}$ to be tangential at every point, so $\mathbf{v}_d$ (and hence $\mathbf{j}$) must also be tangential, changing direction along the circle.
3. The current $I = \int \mathbf{j} \cdot d\mathbf{A}$ is the flux of $\mathbf{j}$ through a cross-section. Since the cross-sectional area and the magnitude $|\mathbf{j}|$ remain constant, $I$ stays the same even as $\mathbf{j}$ rotates.

The key insight here is to separate two ideas: the current $I$ is a scalar that measures the total charge flow per second through a cross-section, and it stays constant because charge cannot pile up in a steady state. The current density $\mathbf{j}$ is a vector that points in the direction of the net flow of positive charge at each point. For a wire bent into a circle, $\mathbf{j}$ must rotate to stay tangent to the wire. What physical agent actually turns the moving charges?

Let’s think about what makes charges move in the first place. In a metal wire, electrons drift under the influence of an electric field $\mathbf{E}$. The relation is $\mathbf{j} = \sigma \mathbf{E}$, where $\sigma$ is the conductivity. So the direction of $\mathbf{j}$ is exactly the direction of the local electric field inside the wire. If $\mathbf{j}$ changes direction along the circle, then $\mathbf{E}$ must also change direction accordingly.

Now, where does this electric field come from? In a steady current, the wire is not a perfect conductor — there is a small electric field along it that drives the current. But for a curved wire, the field cannot be uniform. The charges redistribute themselves on the surface of the wire (surface charges) to create an electric field that is always tangential to the wire, even around bends. This is the same mechanism that guides the current around corners in any circuit.

So the agent is the electric field inside the wire, which is itself maintained by a distribution of surface charges on the wire. The geometry of the wire forces these surface charges to arrange so that $\mathbf{E}$ (and hence $\mathbf{j}$) follows the curve.

Let’s go step by step.

1. Current $I$ is constant — In a steady state, charge does not accumulate anywhere. The same amount of charge per second passes every cross-section. So $I = \int \mathbf{j} \cdot d\mathbf{A}$ is the same at every point along the circle.

2. Current density $\mathbf{j}$ is a vector field — It points in the direction of net positive charge flow. For a thin wire, $\mathbf{j}$ is essentially parallel to the wire axis. As the wire bends into a circle, $\mathbf{j}$ must rotate to stay tangent.

3. Ohm’s law in vector form — For a conductor, $\mathbf{j} = \sigma \mathbf{E}$. This is a local relation. So if $\mathbf{j}$ changes direction, $\mathbf{E}$ must change direction in exactly the same way. The electric field inside the wire is the immediate agent that turns the current density.

4. What creates $\mathbf{E}$? — In a steady current, the electric field inside a wire is not due to a battery alone. The battery provides a potential difference, but the field lines must follow the wire. This is achieved by surface charges on the wire. These charges arrange themselves so that the field inside is tangential to the wire at every point. For a straight wire, surface charges are uniform along the length. For a curved wire, they are non-uniform — more charge accumulates on the inside of the curve to bend the field.

5. The agent is the electric field — So the direct answer is: the electric field $\mathbf{E}$ inside the wire, maintained by surface charges, is responsible for changing the direction of $\mathbf{j}$. The current $I$ remains unaffected because the magnitude of $\mathbf{j}$ adjusts (via the cross-sectional area and conductivity) to keep the total flux constant.

6. Final answer — The agent is the electric field inside the wire, which is set up by a surface charge distribution on the wire that adapts to the curvature.

Method: Reasoning About Current, Current Density, and the Electric Field Inside a Wire

Use this reasoning pattern whenever a question asks "what changes" or "what stays the same" as steady current flows through a conductor of non-trivial shape (bent, curved, or of varying cross-section) — a conceptual question with no numbers to substitute.

Steps

Step 1: Separate the scalar quantity from the vector quantity

Current $I$ is a scalar — the total rate of charge flow through a cross-section. Current density $\mathbf{j}$ is a vector — it has a magnitude AND a direction at every point. Before reasoning further, identify which of these the question is actually asking about; they need not behave the same way as the conductor's shape changes.

Step 2: Use charge conservation to fix the scalar

In a steady state, charge cannot pile up anywhere inside the wire, so the SAME current $I$ must pass through every cross-section, however the wire bends or narrows:

Step 3: Use local Ohm's law to fix the vector's direction

At every point inside a conductor, $\mathbf{j} = \sigma\mathbf{E}$ — the current density points exactly along the local electric field. So wherever $\mathbf{j}$ must turn (e.g. to stay tangent to a curved wire), the electric field $\mathbf{E}$ must turn along with it; the two directions are never independent of each other.

Step 4: Identify what physically produces that field

Ask what agent actually creates and reshapes $\mathbf{E}$ inside the conductor. It is not the battery alone (which only sets the overall potential difference end to end), and not the wire's own magnetic field (which acts perpendicular to the current and cannot redirect it along the wire). It is the small, self-adjusting distribution of surface charge on the conductor, which arranges itself so the interior field stays tangential to the wire at every point, however the wire is shaped.

Step 5: Applying to the specific geometry asked about

Combine Steps 2–4: the total current is unaffected by the conductor's shape (Step 2), the current density's direction bends smoothly because the local electric field bends with it (Step 3), and that bending field is maintained by surface charges reacting to the geometry (Step 4) — never by the source directly, and never by any claim about individual charge carriers' own momentum.